%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT034-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:02:33 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 24
% Syntax : Number of formulae : 100 ( 28 unt; 0 def)
% Number of atoms : 257 ( 11 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 318 ( 161 ~; 157 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t3_58,axiom,
environment(sk1),
file('theBenchmark.p',prove_t3_58) ).
cnf(c_1,plain,
environment(sk1),
inference(clausify,[status(thm)],[prove_t3_58]) ).
fof(a12_57,axiom,
! [VAR_0,VAR_1] :
( decreases(difference(founding_rate(first_movers,VAR_1),founding_rate(efficient_producers,VAR_1)))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a12_57) ).
cnf(c_2,plain,
( decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a12_57]) ).
fof(a10_56,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( subpopulations(first_movers,efficient_producers,VAR_0,VAR_3)
| ~ greater_or_equal(VAR_2,VAR_3)
| ~ greater_or_equal(VAR_3,VAR_1)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a10_56) ).
cnf(c_3,plain,
( subpopulations(first_movers,efficient_producers,A,D)
| ~ greater_or_equal(C,D)
| ~ greater_or_equal(D,B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a10_56]) ).
fof(d1_54,axiom,
! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| VAR_1 != critical_point(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',d1_54) ).
cnf(c_5,plain,
( ~ greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| B != critical_point(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[d1_54]) ).
fof(mp_relationship_of_growth_rates_53,axiom,
! [VAR_0,VAR_1] :
( greater_or_equal(difference(growth_rate(first_movers,VAR_1),growth_rate(efficient_producers,VAR_1)),zero)
| greater(zero,difference(growth_rate(first_movers,VAR_1),growth_rate(efficient_producers,VAR_1)))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_relationship_of_growth_rates_53) ).
cnf(c_6,plain,
( greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| greater(zero,difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_relationship_of_growth_rates_53]) ).
fof(mp_FM_and_EP_members_EP_appeared_49,axiom,
! [VAR_0,VAR_1] :
( greater_or_equal(VAR_1,appear(efficient_producers,VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_FM_and_EP_members_EP_appeared_49) ).
cnf(c_7,plain,
( greater_or_equal(B,appear(efficient_producers,A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_FM_and_EP_members_EP_appeared_49]) ).
fof(mp_symmetry_of_subpopulations_48,axiom,
! [VAR_0,VAR_1] :
( subpopulations(efficient_producers,first_movers,VAR_0,VAR_1)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_symmetry_of_subpopulations_48) ).
cnf(c_8,plain,
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_symmetry_of_subpopulations_48]) ).
fof(mp_critical_time_points_46,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,VAR_1)
| ~ greater(critical_point(VAR_0),VAR_1)
| ~ greater_or_equal(VAR_1,appear(efficient_producers,VAR_0))
| ~ in_environment(VAR_0,critical_point(VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_critical_time_points_46) ).
cnf(c_10,plain,
( in_environment(A,B)
| ~ greater(critical_point(A),B)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_critical_time_points_46]) ).
fof(mp_durations_are_time_intervals_43,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in_environment(VAR_0,VAR_3)
| ~ greater_or_equal(VAR_3,VAR_1)
| ~ greater_or_equal(VAR_2,VAR_3)
| ~ in_environment(VAR_0,VAR_2)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_durations_are_time_intervals_43) ).
cnf(c_13,plain,
( in_environment(A,D)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(C,D)
| ~ in_environment(A,C)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_durations_are_time_intervals_43]) ).
fof(mp_decreasing_function_38,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(difference(growth_rate(first_movers,VAR_2),growth_rate(efficient_producers,VAR_2)),zero)
| ~ decreases(difference(growth_rate(first_movers,VAR_2),growth_rate(efficient_producers,VAR_2)))
| ~ greater(VAR_1,VAR_2)
| ~ greater_or_equal(VAR_2,appear(efficient_producers,VAR_0))
| ~ greater_or_equal(difference(growth_rate(first_movers,VAR_1),growth_rate(efficient_producers,VAR_1)),zero)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_decreasing_function_38) ).
cnf(c_14,plain,
( greater(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)),zero)
| ~ decreases(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)))
| ~ greater(B,C)
| ~ greater_or_equal(C,appear(efficient_producers,A))
| ~ greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_decreasing_function_38]) ).
fof(mp_FM_and_EP_when_EP_appears_36,axiom,
! [VAR_0] :
( subpopulations(first_movers,efficient_producers,VAR_0,appear(efficient_producers,VAR_0))
| ~ in_environment(VAR_0,appear(efficient_producers,VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_FM_and_EP_when_EP_appears_36) ).
cnf(c_15,plain,
( subpopulations(first_movers,efficient_producers,A,appear(efficient_producers,A))
| ~ in_environment(A,appear(efficient_producers,A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_FM_and_EP_when_EP_appears_36]) ).
fof(mp_critical_point_means_FM_and_EP_35,axiom,
! [VAR_0] :
( subpopulations(first_movers,efficient_producers,VAR_0,critical_point(VAR_0))
| ~ in_environment(VAR_0,critical_point(VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_critical_point_means_FM_and_EP_35) ).
cnf(c_16,plain,
( subpopulations(first_movers,efficient_producers,A,critical_point(A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_critical_point_means_FM_and_EP_35]) ).
fof(l3_34,axiom,
! [VAR_0,VAR_1] :
( ~ decreases(difference(disbanding_rate(first_movers,VAR_1),disbanding_rate(efficient_producers,VAR_1)))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l3_34) ).
cnf(c_17,plain,
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l3_34]) ).
fof(mp1_high_growth_rates_33,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( selection_favors(VAR_2,VAR_1,VAR_3)
| ~ greater(growth_rate(VAR_2,VAR_3),growth_rate(VAR_1,VAR_3))
| ~ subpopulations(VAR_1,VAR_2,VAR_0,VAR_3)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp1_high_growth_rates_33) ).
cnf(c_18,plain,
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp1_high_growth_rates_33]) ).
cnf(c_19,plain,
( selection_favors(B,A,C)
| ~ greater(growth_rate(B,C),growth_rate(A,C))
| ~ subpopulations(A,B,sk1,C) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_20,plain,
( ~ decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_21,plain,
( subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| ~ in_environment(sk1,critical_point(sk1)) ),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_22,plain,
( subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1))
| ~ in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_23,plain,
( greater(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| ~ decreases(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)))
| ~ greater(A,B)
| ~ greater_or_equal(B,appear(efficient_producers,sk1))
| ~ greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_24,plain,
( in_environment(sk1,C)
| ~ greater_or_equal(C,A)
| ~ greater_or_equal(B,C)
| ~ in_environment(sk1,B)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_27,plain,
( in_environment(sk1,A)
| ~ greater(critical_point(sk1),A)
| ~ greater_or_equal(A,appear(efficient_producers,sk1))
| ~ in_environment(sk1,critical_point(sk1)) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_29,plain,
( subpopulations(efficient_producers,first_movers,sk1,A)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_30,plain,
( greater_or_equal(A,appear(efficient_producers,sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_31,plain,
( greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero)
| greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_32,plain,
( ~ greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| A != critical_point(sk1) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_33,plain,
( ~ greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| critical_point(sk1) != A ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_36,plain,
( subpopulations(first_movers,efficient_producers,sk1,C)
| ~ greater_or_equal(B,C)
| ~ greater_or_equal(C,A)
| ~ subpopulations(first_movers,efficient_producers,sk1,B)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_37,plain,
( decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A)))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_t3_62,axiom,
~ selection_favors(first_movers,efficient_producers,sk2),
file('theBenchmark.p',prove_t3_62) ).
cnf(c_38,plain,
~ selection_favors(first_movers,efficient_producers,sk2),
inference(clausify,[status(thm)],[prove_t3_62]) ).
fof(prove_t3_61,axiom,
greater(critical_point(sk1),sk2),
file('theBenchmark.p',prove_t3_61) ).
cnf(c_39,plain,
greater(critical_point(sk1),sk2),
inference(clausify,[status(thm)],[prove_t3_61]) ).
fof(prove_t3_60,axiom,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
file('theBenchmark.p',prove_t3_60) ).
cnf(c_40,plain,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
inference(clausify,[status(thm)],[prove_t3_60]) ).
fof(prove_t3_59,axiom,
in_environment(sk1,critical_point(sk1)),
file('theBenchmark.p',prove_t3_59) ).
cnf(c_41,plain,
in_environment(sk1,critical_point(sk1)),
inference(clausify,[status(thm)],[prove_t3_59]) ).
fof(mp_greater_or_equal_52,axiom,
! [VAR_0,VAR_1] :
( greater_or_equal(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',mp_greater_or_equal_52) ).
cnf(c_42,plain,
( greater_or_equal(A,B)
| A != B ),
inference(clausify,[status(thm)],[mp_greater_or_equal_52]) ).
fof(mp_greater_or_equal_51,axiom,
! [VAR_0,VAR_1] :
( greater_or_equal(VAR_0,VAR_1)
| ~ greater(VAR_0,VAR_1) ),
file('theBenchmark.p',mp_greater_or_equal_51) ).
cnf(c_43,plain,
( greater_or_equal(A,B)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal_51]) ).
fof(mp_greater_or_equal_50,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| greater(VAR_0,VAR_1)
| ~ greater_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',mp_greater_or_equal_50) ).
cnf(c_44,plain,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal_50]) ).
fof(mp_positive_growth_rate_difference_41,axiom,
! [VAR_0] :
( greater(growth_rate(first_movers,VAR_0),growth_rate(efficient_producers,VAR_0))
| ~ greater(difference(growth_rate(first_movers,VAR_0),growth_rate(efficient_producers,VAR_0)),zero) ),
file('theBenchmark.p',mp_positive_growth_rate_difference_41) ).
cnf(c_46,plain,
( greater(growth_rate(first_movers,A),growth_rate(efficient_producers,A))
| ~ greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) ),
inference(clausify,[status(thm)],[mp_positive_growth_rate_difference_41]) ).
fof(mp_negative_growth_rate_difference_39,axiom,
! [VAR_0] :
( greater(growth_rate(efficient_producers,VAR_0),growth_rate(first_movers,VAR_0))
| ~ greater(zero,difference(growth_rate(first_movers,VAR_0),growth_rate(efficient_producers,VAR_0))) ),
file('theBenchmark.p',mp_negative_growth_rate_difference_39) ).
cnf(c_48,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) ),
inference(clausify,[status(thm)],[mp_negative_growth_rate_difference_39]) ).
fof(mp_difference_between_founding_rates_37,axiom,
! [VAR_0] :
( decreases(difference(growth_rate(first_movers,VAR_0),growth_rate(efficient_producers,VAR_0)))
| decreases(difference(disbanding_rate(first_movers,VAR_0),disbanding_rate(efficient_producers,VAR_0)))
| ~ decreases(difference(founding_rate(first_movers,VAR_0),founding_rate(efficient_producers,VAR_0))) ),
file('theBenchmark.p',mp_difference_between_founding_rates_37) ).
cnf(c_49,plain,
( decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))) ),
inference(clausify,[status(thm)],[mp_difference_between_founding_rates_37]) ).
cnf(c_50,plain,
( in_environment(sk1,B)
| ~ greater_or_equal(B,A)
| ~ greater_or_equal(A,B)
| ~ in_environment(sk1,A) ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_52,plain,
( in_environment(sk1,A)
| ~ greater(critical_point(sk1),A)
| ~ greater_or_equal(A,appear(efficient_producers,sk1)) ),
inference(resolve,[status(thm)],[c_41,c_27]) ).
cnf(c_53,plain,
subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1)),
inference(resolve,[status(thm)],[c_41,c_21]) ).
cnf(c_58,plain,
~ greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1))),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_61,plain,
( greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero)
| ~ decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| ~ greater(critical_point(sk1),A)
| ~ greater_or_equal(A,appear(efficient_producers,sk1))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero) ),
inference(resolve,[status(thm)],[c_41,c_23]) ).
cnf(c_62,plain,
greater_or_equal(A,A),
inference(xxres,[status(thm)],[c_42]) ).
cnf(c_63,plain,
greater_or_equal(critical_point(sk1),sk2),
inference(resolve,[status(thm)],[c_43,c_39]) ).
cnf(c_66,plain,
( in_environment(sk1,A)
| ~ greater_or_equal(A,critical_point(sk1))
| ~ greater_or_equal(critical_point(sk1),A) ),
inference(resolve,[status(thm)],[c_50,c_41]) ).
cnf(c_71,plain,
( subpopulations(first_movers,efficient_producers,sk1,B)
| ~ greater_or_equal(critical_point(sk1),B)
| ~ greater_or_equal(B,A)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_53,c_36]) ).
cnf(c_74,plain,
( greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) ),
inference(resolve,[status(thm)],[c_53,c_31]) ).
cnf(c_75,plain,
greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)),
inference(resolve,[status(thm)],[c_53,c_30]) ).
cnf(c_83,plain,
~ greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))),
inference(resolve,[status(thm)],[c_48,c_58]) ).
cnf(c_84,plain,
greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero),
inference(resolve,[status(thm)],[c_83,c_74]) ).
cnf(c_85,plain,
( greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero)
| ~ decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| ~ greater(critical_point(sk1),A)
| ~ greater_or_equal(A,appear(efficient_producers,sk1)) ),
inference(resolve,[status(thm)],[c_84,c_61]) ).
cnf(c_87,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| ~ greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(resolve,[status(thm)],[c_62,c_52]) ).
cnf(c_97,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(resolve,[status(thm)],[c_75,c_44]) ).
cnf(c_105,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| ~ greater_or_equal(appear(efficient_producers,sk1),critical_point(sk1)) ),
inference(resolve,[status(thm)],[c_66,c_75]) ).
cnf(c_126,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(resolve,[status(thm)],[c_97,c_87]) ).
cnf(c_222,plain,
( greater_or_equal(A,B)
| B != A ),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_128,plain,
( greater_or_equal(appear(efficient_producers,sk1),critical_point(sk1))
| in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(resolve,[status(thm)],[c_126,c_222]) ).
cnf(c_223,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(resolve,[status(thm)],[c_128,c_105]) ).
cnf(c_153,plain,
in_environment(sk1,appear(efficient_producers,sk1)),
inference(copy,[status(thm)],[c_223]) ).
cnf(c_154,plain,
subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)),
inference(resolve,[status(thm)],[c_153,c_22]) ).
cnf(c_166,plain,
( subpopulations(first_movers,efficient_producers,sk1,A)
| ~ greater_or_equal(critical_point(sk1),A)
| ~ greater_or_equal(A,appear(efficient_producers,sk1)) ),
inference(resolve,[status(thm)],[c_154,c_71]) ).
cnf(c_224,plain,
( greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| ~ greater(critical_point(sk1),sk2) ),
inference(resolve,[status(thm)],[c_85,c_40]) ).
cnf(c_177,plain,
( greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) ),
inference(resolve,[status(thm)],[c_39,c_224]) ).
cnf(c_225,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ greater_or_equal(critical_point(sk1),sk2) ),
inference(resolve,[status(thm)],[c_166,c_40]) ).
cnf(c_199,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(resolve,[status(thm)],[c_63,c_225]) ).
cnf(c_203,plain,
decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))),
inference(resolve,[status(thm)],[c_199,c_37]) ).
cnf(c_208,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(resolve,[status(thm)],[c_199,c_29]) ).
cnf(c_209,plain,
~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(resolve,[status(thm)],[c_199,c_20]) ).
cnf(c_226,plain,
( selection_favors(first_movers,efficient_producers,sk2)
| ~ greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_208,c_19]) ).
cnf(c_211,plain,
~ greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),
inference(resolve,[status(thm)],[c_38,c_226]) ).
cnf(c_219,plain,
~ greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero),
inference(resolve,[status(thm)],[c_46,c_211]) ).
cnf(c_220,plain,
~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))),
inference(resolve,[status(thm)],[c_219,c_177]) ).
cnf(c_227,plain,
( decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| ~ decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))) ),
inference(resolve,[status(thm)],[c_49,c_209]) ).
cnf(c_228,plain,
~ decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))),
inference(resolve,[status(thm)],[c_227,c_220]) ).
cnf(c_221,plain,
$false,
inference(resolve,[status(thm)],[c_203,c_228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT034-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n019.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Sat Sep 26 00:06:00 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.39 % Process 4046164 was started by sandbox2 on n019,
% 0.09/10.39 % Sat Sep 26 00:06:00 2026
% 0.09/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/10.39
% 0.09/10.39 % From the command line: assign(max_seconds, 300).
% 0.14/10.42
% 0.14/10.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.42
% 0.14/10.42 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/10.42 % Length of proof is 69.
% 0.14/10.42 % Level of proof is 15.
% 0.14/10.42 % Maximum clause weight is 57.000.
% 0.14/10.42 % Given clauses 116.
% 0.14/10.42
% 0.14/10.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------